For each $\alpha >2$ there is an infinite binary word with critical exponent $\alpha$.

Currie, James D., and Rampersad, Narad. "For each there is an infinite binary word with critical exponent .." The Electronic Journal of Combinatorics [electronic only] 15.1 (2008): Research Paper N34, 5 p.-Research Paper N34, 5 p.. <http://eudml.org/doc/117202>.

@article{Currie2008,
author = {Currie, James D., Rampersad, Narad},
journal = {The Electronic Journal of Combinatorics [electronic only]},
keywords = {combinatorics on words; repetitions; critical exponent},
language = {eng},
number = {1},
pages = {Research Paper N34, 5 p.-Research Paper N34, 5 p.},
publisher = {Prof. André Kündgen, Deptartment of Mathematics, California State University San Marcos, San Marcos},
title = {For each there is an infinite binary word with critical exponent .},
url = {http://eudml.org/doc/117202},
volume = {15},
year = {2008},
}

TY - JOUR
AU - Currie, James D.
AU - Rampersad, Narad
TI - For each there is an infinite binary word with critical exponent .
JO - The Electronic Journal of Combinatorics [electronic only]
PY - 2008
PB - Prof. André Kündgen, Deptartment of Mathematics, California State University San Marcos, San Marcos
VL - 15
IS - 1
SP - Research Paper N34, 5 p.
EP - Research Paper N34, 5 p.
LA - eng
KW - combinatorics on words; repetitions; critical exponent
UR - http://eudml.org/doc/117202
ER -